Solving Singly Constrained Transshipment Problems

Glover, Fred; Karney, David; Klingman, Darwin; Russell, Robert A.

doi:10.1287/trsc.12.4.277

Cited by 38 publications

(12 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We B. Cao can now solve a classical transportation problem efficiently. Some authors extended the work to network problems with side constraints and generalized network problems with side constraints, see Klingman and Russel [6], Glover, Karney, Klingman and Russel [4], Thompson and Sethi [8]. The problems discussed in these papers were network problems or generalized network problems with linear side constraints.…”

Section: Introductionmentioning

confidence: 99%

Transportation problem with nonlinear side constraints a branch and bound approach

Cao

1992

ZOR - Methods and Models of Operations Research

View full text Add to dashboard Cite

Abstract:In a container terminal management, we are often confronted with the following problem:how to assign a reasonable depositing position for an arriving container, so that the efficiency of searching for and loading of a container later can be increased. In this paper, the problem is modeled as a transportation problem with nonlinear side constraints (TPNSC). The reason of nonlinear side constraints arising is that some kinds of containers cannot be stacked in the same row (the space of storage yard is properly divided into several rows). A branch and bound algorithm is designed to solve this problem. The algorithm is based on the idea of using disjunctive arcs (branches) for resolving conflicts that are created whenever some conflicting kinds of containers are deposited in the same row. During the branch and bound, the candidate problems are transformed into classical transportation problems, so that the efficient transportation algorithm can be applied, at the same time the reoptimization technique is employed during the branch and bound. Further, we design a heuristic to obtain a feasible initial solution for TPNSC in order to prune some candidates as early and/or as much as possible. We report computational results on randomly generated problems,

show abstract

Section: Introductionmentioning

confidence: 99%

Transportation problem with nonlinear side constraints a branch and bound approach

Cao

1992

ZOR - Methods and Models of Operations Research

View full text Add to dashboard Cite

show abstract

“…If at optimality of the continuous relaxation the solution is not integral, then an integer solution can be obtained by forcing the slack variable, s, into the basis. This idea has been used by Klingman and Russell [22] and by Glover, Karney, Klingman, and Russell [13]. For comparison purposes, Professor Mazzola of Duke University allowed us restricted access to his exact branch-and-bound code for this problem (see [24]).…”

Section: Empirical Analysismentioning

confidence: 99%

“…Glover, Karney, Klingman and Russell [ 13] developed a primal simplex procedure to solve the transshipment problem with an arbitrary additional constraint. They presented efficient pricing and column update methods along with a fast technique to obtain an integer solution for this problem.…”

Section: Introductionmentioning

confidence: 99%

The singly constrained assignment problem: An AP basis algorithm

Kennington

Mohammadi

1995

Comput Optim Applic

View full text Add to dashboard Cite

Abstract. This manuscript presents a specialized primal simplex algorithm to obtain near optimal integer solutions for the singly constrained assignment problem. An optimal solution for the continuous relaxation of the problem is obtained by generalizing the alternating basis algorithm of Barr, G/over, and Klingman for the pure assignment problem. Near optimal integer solutions are obtained by pivoting into the optimal basis the slack variable associated with the side constraint. Our empirical analysis indicated that for our test problems the software implementation of this algorithm was six times faster than CPLEX and four times faster than NETSIDE (a specialized code for network problems with side constraints). The integer solutions obtained in our tests were typically within 2% of the optimum of the continuous relaxation.

show abstract

“…Klingman and Russell [21] developed a simplex based method for the transportation problem with a single side constraint and Glover, Karney, Klingman, and Russell [13] developed a simplex based method for the transshipment problem with a single side constraint. Authors of both papers state that codes based on their procedures are significantly faster than the LP code APEX-III and they both obtain an integer solution for the problem with an inequality side constraint by pivoting into the basis the slack variable associated with the side constraint.…”

Section: (Ij)eementioning

confidence: 99%

The singly constrained assignment problem: A Lagrangian relaxation heuristic algorithm

Kennington

Mohammadi

1994

Comput Optim Applic

View full text Add to dashboard Cite

Abstract. This manuscript presents a new heuristic algorithm to find near optimal integer solutions for the singly constrained assignment problem. The method is based on Lagrangian duality theory and involves solving a series of pure assignment problems. The software implementation of this heuristic, ASSIGN+ 1, successfully solved problems having one-half million binary variables (assignment arcs) in tess than 17 minutes of wall clock time on a Sequent Symmetry $81 using a single processor. In computational comparisons with MPSX and OSL on an IBM 3081D, the specialized software was from 100 to 1,000 times faster. In computational comparisons with the specialized code of Mazzola and Neebe, we found that ASSIGN+I was 40 times faster. In computational comparisons with our best alternating path specialized code, we found that ASSIGN+ 1 was more than three times faster than that code. This new software proved to be very robust as well as fast. The robustness is due to an elaborate scheme used to update the Lagrangean multipliers and the speed is due to the fine code used to solve the pure assignment problems. We also present a modification of the algorithm for the case in which the number of jobs exceeds the number of men along with an empirical analysis of the modified software.

show abstract

Solving Singly Constrained Transshipment Problems

Cited by 38 publications

References 24 publications

Transportation problem with nonlinear side constraints a branch and bound approach

Transportation problem with nonlinear side constraints a branch and bound approach

The singly constrained assignment problem: An AP basis algorithm

The singly constrained assignment problem: A Lagrangian relaxation heuristic algorithm

Contact Info

Product

Resources

About